Stress profiles of glass-based articles having improved drop performance

ABSTRACT

Glass-based articles comprise stress profiles providing improved drop performance. A glass-based substrate comprises: a glass transition temperature (T g ), a liquid fragility index (m), and fictive temperature (T f ), wherein T g  is less than or equal to 650° C., a value of T f  minus T g  is greater than or equal to −30° C., and m is greater than or equal to 25. A stress relaxation rate is greater than or equal to 10%, or 20% or more. The articles can comprise a lithium-based aluminosilicate composition and a fracture toughness that is greater than or equal to 0.75 MPa*m 0.5 . The stress profiles comprise: a spike region extending from the first surface to a knee; and a tail region extending from the knee to a center of the glass-based article, the tail region comprising: a negative curvature region wherein a second derivative of stress as a function of depth is negative; a depth of compression (DOC) that is greater than or equal to 0.22 t, and a parabolic region originating at the DOC and extending to the center of the glass-based article.

This application claims the benefit of priority under 35 U.S.C. § 119 ofU.S. Provisional Application Ser. No. 63/083,287 filed on Sep. 25, 2020,the content of which is relied upon and incorporated herein by referencein its entirety.

BACKGROUND Field

The present specification generally relates to stress profiles ofglass-based articles suitable for use as cover glass for electronicdevices. More particularly, the specification relates to improved stressprofiles and methods of providing lithium-containing aluminosilicateglasses with improved drop performance.

Technical Background

The mobile nature of portable devices, such as smart phones, tablets,portable media players, personal computers, and cameras, makes thesedevices particularly vulnerable to accidental dropping on hard surfaces,such as the ground. These devices typically incorporate cover glasses,which may become damaged upon impact with hard surfaces. In many ofthese devices, the cover glasses function as display covers, and mayincorporate touch functionality, such that use of the devices isnegatively impacted when the cover glasses are damaged.

There are two major failure modes of cover glass when the associatedportable device is dropped on a hard surface. One of the modes isflexure failure, which is caused by bending of the glass when the deviceis subjected to dynamic load from impact with the hard surface. Theother mode is sharp contact failure, which is caused by introduction ofdamage to the glass surface. Impact of the glass with rough hardsurfaces, such as asphalt, granite, etc., can result in sharpindentations in the glass surface. These indentations become failuresites in the glass surface from which cracks may develop and propagate.

Chemical treatment is a strengthening method to impart a desired and/orengineered stress profile having one or more of the followingparameters: compressive stress (CS), depth of compression (DOC), andmaximum central tension (CT). Many glass-based articles, including thosewith engineered stress profiles, have a compressive stress that ishighest or at a peak at the glass surface and reduces from a peak valuemoving away from the surface, and there is zero stress at some interiorlocation of the glass article before the stress in the glass articlebecomes tensile. Chemical strengthening by ion exchange (IOX) ofalkali-containing glass is a proven methodology in this field.

Glass-based articles, specifically glasses, can be made more resistantto flexure failure by traditional ion-exchange techniques, which caninvolve inducing compressive stress in the glass surface. However, theion-exchanged glass can still be vulnerable to dynamic sharp contact,owing to the high stress concentration caused by local indentations inthe glass from the sharp contact.

It has been a continuous effort for glass makers and handheld devicemanufacturers to improve the resistance of handheld devices to sharpcontact failure. Solutions range from coatings on the cover glass tobezels that prevent the cover glass from impacting the hard surfacedirectly when the device drops on the hard surface. However, due to theconstraints of aesthetic and functional requirements, it is verydifficult to completely prevent the cover glass from impacting the hardsurface.

There is a need for improved stress profiles that result in excellentdrop performance.

SUMMARY

Aspects of the disclosure pertain to glass-based articles and methodsfor their manufacture.

In an aspect, a glass-based substrate comprises: a glass transitiontemperature (T_(g)), a liquid fragility index (m), and fictivetemperature (T_(f)), wherein T_(g) is less than or equal to 650° C., avalue of T_(f) minus T_(g) is greater than or equal to −30° C., and m isgreater than or equal to 25.

In an embodiment, the glass-based substrate comprises: a stressrelaxation rate of greater than or equal to 10%. In an embodiment, T_(g)is greater than or equal to 550° C., the value of T_(f) minus T_(g) isless than or equal to 100° C., and m is greater than or equal to 25. Inan embodiment, m is greater than or equal to 30. In an embodiment, m isless than or equal to 60.

In an embodiment, the glass-based substrate further comprises: alithium-based aluminosilicate composition and a fracture toughness thatis greater than or equal to 0.75 MPa*m^(0.5). In an embodiment, thelithium-based aluminosilicate composition comprises a lithium oxide(Li₂O) content of greater than 8 mol %. In an embodiment, thelithium-based aluminosilicate composition comprises a molar ratio ofsodium oxide (Na₂O) to lithium oxide (Li₂O) of less than 1.0. In anembodiment, the molar ratio of sodium oxide (Na₂O) to lithium oxide(Li₂O) is less than or equal to 0.63. In an embodiment, thelithium-based aluminosilicate composition comprises potassium oxide(K₂O) and phosphorus pentoxide (P₂O₅) in an amount that is less than 2mol % of the composition. In an embodiment, the lithium-basedaluminosilicate composition comprises: 50 mol % to 69 mol % SiO₂; 12.5mol % to 25 mol % Al₂O₃; 0 mol % to 8 mol % B₂O₃; greater than 0 mol %to 4 mol % CaO; greater than 0 mol % to 17.5 mol % MgO; 0.5 mol % to 8mol % Na₂O; 0 mol % to 2.5 mol % La₂O₃; and greater than 8 mol % to 18mol % Li₂O.

In an aspect, a method of manufacturing a glass-based article comprises:preparing a glass composition; exposing the glass composition to aprocess to form a glass-based substrate comprising: a glass transitiontemperature (T_(g)), a liquid fragility index (m), and fictivetemperature (T_(f)), wherein T_(g) is less than or equal to 650° C., thedifference between T_(f) and T_(g) is greater than or equal to −30° C.,and m is greater than or equal to 25; and exposing the glass-basedsubstrate to ion exchange conditions of less than or equal to 550° C. toform a glass-based article comprising a stress relaxation rate that isgreater than or equal to 10%. In an embodiment, the process to form theglass-based substrate comprises a float process, a down-draw process, afusion-formable process, a slot-draw process, or a roll-form process. Inan embodiment, the process further comprises an annealing step.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments described herein, including the detailed description whichfollows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description describe various embodiments and areintended to provide an overview or framework for understanding thenature and character of the claimed subject matter. The accompanyingdrawings are included to provide a further understanding of the variousembodiments, and are incorporated into and constitute a part of thisspecification. The drawings illustrate the various embodiments describedherein, and together with the description serve to explain theprinciples and operations of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying figures, which are incorporated in and constitute apart of this specification, illustrate several embodiments describedbelow.

FIG. 1 schematically depicts a cross-section of a glass havingcompressive stress layers on surfaces thereof according to embodimentsdisclosed and described herein;

FIG. 2 is a generalized schematic stress profile graph of stress (MPa)versus normalized position (z/thickness) from a surface for anembodiment of a glass-based article;

FIG. 3A is a plan view of an exemplary electronic device incorporatingany of the glass articles disclosed herein;

FIG. 3B is a perspective view of the exemplary electronic device of FIG.3A;

FIG. 4 is a plot of stress (MPa) versus depth (micrometers) from asurface for embodiments of a glass-based article and comparativeexamples;

FIG. 5 is a plot of a sodium dioxide (Na₂O) concentration versus depthfor an embodiment;

FIG. 6 is a plot of applied fracture stress (MPa) versus grit for anembodiment of a glass-based article;

FIG. 7 is a plot of stress (MPa) versus depth (micrometers) from asurface for embodiments of a glass-based article and comparativeexamples;

FIG. 8 is graph of the second derivative of the stress profile plot ofFIG. 6;

FIG. 9 is an excerpt of a stress profile according to embodiments of aglass-based article;

FIG. 10 is a schematic view of an apparatus that introduces damage to aglass article via impact with an impacting object;

FIGS. 11-14 are stress relaxation rates according to embodiments ofglass-based substrates; and

FIG. 15 is a plot of T_(g), minimum fragility (m) and lowest T_(f)-T_(g)to insure sufficient stress relaxation for T_(IOX) of less than or equalto 500° C.

DETAILED DESCRIPTION

Before describing several exemplary embodiments, it is to be understoodthat the disclosure is not limited to the details of construction orprocess steps set forth in the following disclosure. The disclosureprovided herein is capable of other embodiments and of being practicedor being carried out in various ways.

Reference throughout this specification to “one embodiment,” “certainembodiments,” “various embodiments,” “one or more embodiments” or “anembodiment” means that a particular feature, structure, material, orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the disclosure. Thus, the appearances ofthe phrases such as “in one or more embodiments,” “in certainembodiments,” “in various embodiments,” “in one embodiment” or “in anembodiment” in various places throughout this specification are notnecessarily referring to the same embodiment, or to only one embodiment.Furthermore, the particular features, structures, materials, orcharacteristics may be combined in any suitable manner in one or moreembodiments.

Definitions and Measurement Techniques

The terms “glass-based article” and “glass-based substrates” are used toinclude any object made wholly or partly of glass, such as glass orglass-ceramic materials. Laminated glass-based articles includelaminates of glass and non-glass materials, laminates of glass andcrystalline materials.

A “base composition” is a chemical make-up of a substrate prior to anyion exchange (IOX) treatment. That is, the base composition is undopedby any ions from IOX. A composition at the center of a glass-basedarticle that has been IOX treated is typically the same as the basecomposition when IOX treatment conditions are such that ions suppliedfor IOX do not diffuse into the center of the substrate. In one or moreembodiments, a central composition at the center of the glass articlecomprises the base composition.

It is noted that the terms “substantially” and “about” may be utilizedherein to represent the inherent degree of uncertainty that may beattributed to any quantitative comparison, value, measurement, or otherrepresentation. These terms are also utilized herein to represent thedegree by which a quantitative representation may vary from a statedreference without resulting in a change in the basic function of thesubject matter at issue. Thus, for example, a glass-based article thatis “substantially free of MgO” is one in which MgO is not actively addedor batched into the glass-based article, but may be present in verysmall amounts as a contaminant. As used herein, the term “about” meansthat amounts, sizes, formulations, parameters, and other quantities andcharacteristics are not and need not be exact, but may be approximateand/or larger or smaller, as desired, reflecting tolerances, conversionfactors, rounding off, measurement error and the like, and other factorsknown to those of skill in the art. When the term “about” is used indescribing a value or an end-point of a range, the disclosure should beunderstood to include the specific value or end-point referred to.Whether or not a numerical value or end-point of a range in thespecification recites “about,” the numerical value or end-point of arange is intended to include two embodiments: one modified by “about,”and one not modified by “about.” It will be further understood that theendpoints of each of the ranges are significant both in relation to theother endpoint, and independently of the other endpoint.

Unless otherwise specified, all compositions described herein areexpressed in terms of mole percent (mol %) on an oxide basis.

A “stress profile” is stress as a function of thickness across aglass-based article. A compressive stress region extends from a firstsurface to a depth of compression (DOC) of the article, and is a regionwhere the article is under compressive stress. A central tension regionextends from the DOC to include the region where the article is undertensile stress.

As used herein, depth of compression (DOC) refers to the depth at whichthe stress within the glass-based article changes from compressive totensile stress. At the DOC, the stress crosses from a positive(compressive) stress to a negative (tensile) stress and thus exhibits astress value of zero. According to the convention normally used inmechanical arts, compression is expressed as a negative (<0) stress andtension is expressed as a positive (>0) stress. Throughout thisdescription, however, positive values of stress are compressive stress(CS), which are expressed as a positive or absolute value—i.e., asrecited herein, CS=|CS|. Additionally, negative values of stress aretensile stress. But when used with the term “tensile”, stress or centraltension (CT) may be expressed as a positive value, i.e., CT=|CT|.Central tension (CT) refers to tensile stress in a central region or acentral tension region of the glass-based article. Maximum centraltension (maximum CT or CT_(max)) may occur in the central tensionregion, such as nominally at 0.5·t, where t is the article thickness,which allows for variation from exact center of the location of themaximum tensile stress. Peak tension (PT) refers to maximum tensionmeasured, which may or may not be at the center of the article.

A “knee” of a stress profile is a depth of an article where the slope ofthe stress profile transitions from steep to gradual. The knee may referto a transition area over a span of depths where the slope is changing.The knee stress CS_(k) is defined as the value of compressive stressthat the deeper portion of the CS profile extrapolates to at the depthof spike (DOL_(k)). The DOL_(k) is reported as measured by asurface-stress meter by known methods. A schematic representation of astress profile including a knee stress is provided in FIG. 2.

A non-zero metal oxide concentration that varies from the first surfaceto a depth of layer (DOL) with respect to the metal oxide or that variesalong at least a substantial portion of the article thickness (t)indicates that a stress has been generated in the article as a result ofion exchange. The variation in metal oxide concentration may be referredto herein as a metal oxide concentration gradient. The metal oxide thatis non-zero in concentration and varies from the first surface to a DOLor along a portion of the thickness may be described as generating astress in the glass-based article. The concentration gradient orvariation of metal oxides is created by chemically strengthening aglass-based substrate in which a plurality of first metal ions in theglass-based substrate is exchanged with a plurality of second metalions.

As used herein, the terms “depth of exchange”, “depth of layer” (DOL),“chemical depth of layer”, and “depth of chemical layer” may be usedinterchangeably, describing in general the depth at which ion exchangefacilitated by an ion exchange process (IOX) takes place for aparticular ion. DOL refers to the depth within a glass-based article(i.e., the distance from a surface of the glass-based article to itsinterior region) at which an ion of a metal oxide or alkali metal oxide(e.g., the metal ion or alkali metal ion) diffuses into the glass-basedarticle where the concentration of the ion reaches a minimum value, asdetermined by Glow Discharge-Optical Emission Spectroscopy (GD-OES)). Insome embodiments, the DOL is given as the depth of exchange of theslowest-diffusing or largest ion introduced by an ion exchange (IOX)process. DOL with respect to potassium (DOL_(K)) is the depth at whichthe potassium content of the glass article reaches the potassium contentof the underlying substrate. DOL with respect to sodium (DOL_(Na)) isthe depth at which the sodium content of the glass article reaches thesodium content of the underlying substrate.

Unless otherwise specified, CT and CS are expressed herein inmegaPascals (MPa), thickness is express in millimeters and DOC and DOLare expressed in microns (micrometers).

Compressive stress (including surface/peak CS, CS_(max)) and DOL_(sp)are measured by surface stress meter (FSM) using commercially availableinstruments such as the FSM-6000, manufactured by Orihara IndustrialCo., Ltd. (Japan). Surface stress measurements rely upon the accuratemeasurement of the stress optical coefficient (SOC), which is related tothe birefringence of the glass. SOC in turn is measured according toProcedure C (Glass Disc Method) described in ASTM standard C770-16,entitled “Standard Test Method for Measurement of Glass Stress-OpticalCoefficient,” the contents of which are incorporated herein by referencein their entirety.

The maximum central tension (CT) or peak tension (PT) and stressretention values are measured using a scattered light polariscope(SCALP) technique known in the art. The Refracted near-field (RNF)method or SCALP may be used to measure the stress profile and the depthof compression (DOC). When the RNF method is utilized to measure thestress profile, the maximum CT value provided by SCALP is utilized inthe RNF method. In particular, the stress profile measured by RNF isforce balanced and calibrated to the maximum CT value provided by aSCALP measurement. The RNF method is described in U.S. Pat. No.8,854,623, entitled “Systems and methods for measuring a profilecharacteristic of a glass sample”, which is incorporated herein byreference in its entirety. In particular, the RNF method includesplacing the glass article adjacent to a reference block, generating apolarization-switched light beam that is switched between orthogonalpolarizations at a rate of from 1 Hz to 50 Hz, measuring an amount ofpower in the polarization-switched light beam and generating apolarization-switched reference signal, wherein the measured amounts ofpower in each of the orthogonal polarizations are within 50% of eachother. The method further includes transmitting thepolarization-switched light beam through the glass sample and referenceblock for different depths into the glass sample, then relaying thetransmitted polarization-switched light beam to a signal photodetectorusing a relay optical system, with the signal photodetector generating apolarization-switched detector signal. The method also includes dividingthe detector signal by the reference signal to form a normalizeddetector signal and determining the profile characteristic of the glasssample from the normalized detector signal.

Fracture toughness (K_(1C)) represents the ability of a glasscomposition to resist fracture. Fracture toughness is measured on anon-strengthened glass article, such as measuring the K_(1C) value priorto ion exchange (IOX) treatment of the glass article, therebyrepresenting a feature of a glass substrate prior to IOX. The fracturetoughness test methods described herein are not suitable for glassesthat have been exposed to IOX treatment. But, fracture toughnessmeasurements performed as described herein on the same glass prior toIOX treatment (e.g., glass substrates) correlate to fracture toughnessafter IOX treatment, and are accordingly used as such. The chevronnotched short bar (CNSB) method utilized to measure the K_(1C) value isdisclosed in Reddy, K. P. R. et al, “Fracture Toughness Measurement ofGlass and Ceramic Materials Using Chevron-Notched Specimens,” J. Am.Ceram. Soc., 71 [6], C-310-C-313 (1988) except that Y*_(m) is calculatedusing equation 5 of Bubsey, R. T. et al., “Closed-Form Expressions forCrack-Mouth Displacement and Stress Intensity Factors forChevron-Notched Short Bar and Short Rod Specimens Based on ExperimentalCompliance Measurements,” NASA Technical Memorandum 83796, pp. 1-30(October 1992). The double torsion method and fixture utilized tomeasure the K_(1C) value is described in Shyam, A. and Lara-Curzio, E.,“The double-torsion testing technique for determination of fracturetoughness and slow crack growth of materials: A review,” J. Mater. Sci.,41, pp. 4093-4104, (2006). The double torsion measurement methodgenerally produces K_(1C) values that are slightly higher than thechevron notched short bar method. Unless otherwise specified, allfracture toughness values were measured by chevron notched short bar(CNSB) method.

Stress relaxation ratio (SR) of measured relaxed stress (σ_(r)) totheoretical unrelaxed stress (σ_(o)) in glasses that have been exposedto IOX treatment refers to the ratio of final measured relaxed stressafter IOX to theoretical unrelaxed stress that is expected from a stressprofile based on ideal conditions for diffusion based on a complementaryerror function (erfc(x)). A SR has a value of less than 1 to greaterthan 0. A stress relaxation rate of a substrate or an article is apercentage of reduction of a theoretical unrelaxed stress. For example,for a theoretical unrelaxed stress (σ_(o)) of 100 MPa and a measuredrelaxed stress (σ_(r)) of 90 MPa, the stress relaxation rate is 10%, or1 minus the SR times 100.

Theoretical unrelaxed stress (σ_(o)) is determined based on a measuredion concentration through thickness of an IOX-treated article, which isentered into the following linear elastic equation.

${{\sigma^{\Omega^{\prime}}\left( {z,T} \right)} = {\frac{BE}{1 - v}\left\lbrack {{C_{avg}(T)} - {C\left( {z,T} \right)}} \right\rbrack}},$

where z is location and T is through the thickness of the article, C isconcentration, B is linear lattice dilation coefficient, E is Young'smodulus, and v is Poisson's ratio. Based on ionic radius of Li+ (0.08nm), Na+ (0.102 nm), and K+ (0.0138 nm), one mol % percent of Li+→Na+IOX causes about 60% growth when compared to one mol % percent ofNa+→K+, therefore a value of 0.6 ppk/mol % Li+→Na+ was used for B. Forglasses of interest, E is generally in the range of greater than orequal to 60 to less than or equal to 90 GPa; and v is generally greaterthan or equal to 0.2 to less than or equal to 0.24.

Measured relaxed stress (σ_(r)) is determined from a surface stressmeasurement, excluding any spike or steep surface profile, conducted by,for example, Refractive Near Field (RNF) method.

Molten glass has different structures at different temperatures. Thisstructure may be frozen into a solidified (or solid) glass, depending onthe thermal treatment to which the glass is exposed. As used herein,fictive temperature (T_(f)) of a solid glass is the temperature of amolten glass having a structure that is the same as that of the solidglass. A discussion of fictive temperature can be found in, for example,Mauro, et al., “Fictive Temperature and the Glassy State,” J. Am. Ceram.Soc., 2009, 92:75-86, the content of which in its entirety isincorporated herein by reference. In accordance with the presentdisclosure, the calculation of the fictive temperature associated withthe thermal history and glass properties of a particular glasscomposition can follow established methods. T_(f) can be determinedaccording to the Guo methodology of “Unified approach for determiningenthalpic fictive temperature of glasses with arbitrary thermalhistory.” Journal of Non-Crystalline solids. 357 (2011) 3230-3236 (Guoet al.), the contents of which are incorporated herein by reference intheir entirety. The Guo methodology generates first and second upscansof heat capacity versus temperature curves using differential scanningcalorimetry at a DSC upscan rate of 10 K/min. The three-step procedureincludes: (σ) first, calculating fictive temperature of a rejuvenatedglass, T_(f), on the second upscan using area-matching; (b) second,calculating the area between the two DSC upscan curves, which gives thedifference between the enthalpies of as-formed (H₁) and rejuvenatedglasses (H₂); and (c) finally, determining the fictive temperature ofthe as-formed glass, T_(f1), by area-matching using Eq. (A):

$\begin{matrix}{{\int\limits_{T_{f2}}^{T_{f1}}{\left( {C_{p\mspace{14mu}{liquid}} - C_{p\mspace{14mu}{glass}}} \right){dT}}} = {\int\limits_{0}^{\infty}{\left( {C_{p2} - C_{p1}} \right){{dT}.}}}} & {(A).}\end{matrix}$

Unless otherwise specified, all T_(f) values were determined by the Guomethodology.

As used herein, the glass transition temperature (T_(g)) of a materialis the temperature at which it has an equilibrium viscosity of 10¹²Pa-s. Unless otherwise specified, all T_(g) values were determined froma viscosity vs temperature curve generated in accordance with ASTMC1350M-96 (2019) (“Standard Test Method for Measurement of Viscosity ofGlass Between Softening Point and Annealing Range (Approximately 10⁸Pa·s to approximately 10¹³ Pa·s) by Beam Bending”).

As used herein, liquid fragility index (m) of a material is a rate ofviscosity change as a function of temperature at its glass transitiontemperature (T_(g)). The liquid fragility index (m) for composition (x)is defined by:

${m(x)} = \left. \frac{{\partial\log_{10}}\eta_{eq}\mspace{14mu}\left( {T,x} \right)}{\partial\left( {{{Tg}(x)}/T} \right)} \middle| {}_{T = {{Tg}{(x)}}}. \right.$

A viscosity vs temperature curve is generated using one or moreviscometers. The value of liquid fragility index (m) is the slope of thelog(viscosity) vs 1/T curve at T=T_(g). Unless otherwise specified, allm values were determined from a viscosity vs temperature curve generatedin accordance with the following test methods in combination: ASTMC-965-96 (2017) (“Standard Practice for Measuring Viscosity of GlassAbove the Softening Point); STM C1351M-96(2017) (“Standard Test Methodfor Measurement of Viscosity of Glass Between 10⁴ Pa·s and 10⁸ Pa·s byViscous Compression of a Solid Right Cylinder); and ASTM C1350M-96(2019)(“Standard Test Method for Measurement of Viscosity of Glass BetweenSoftening Point and Annealing Range (Approximately 10⁸ Pa·s toApproximately 10¹³ Pa·s) by Beam Bending”).

Both the glass transition temperature (T_(g)) for composition x and thecomposition's fragility can be expressed as expansions which employempirically-determined fitting coefficients. Such expansions arediscussed in detail in co-pending, commonly-assigned U.S. patentapplication Ser. No. 12/896,355, entitled “METHODS AND APPARATUS FORPREDICTING GLASS PROPERTIES,” which was filed on Oct. 1, 2010, thecontent of which in its entirety is hereby incorporated herein byreference.

General Overview of Properties of Glass-Based Articles

Glass-based articles herein are designed to have improved dropperformance for high damage resistant glasses. Glass-based articlesherein are designed with compositions and characteristics to leveragestress relaxation. This results in stress profiles having an S-shapebefore a depth of compression (DOC) and a parabolic shape after the DOC.

Glass-based substrates are designed herein to achieve the desiredS-shape profile over a reasonable ion exchange (IOX) treatment time andbelow a chosen IOX treatment temperature. In one or more embodiments,the glass stress-based substrates achieve a stress relaxation rate ofgreater than or equal to 10%, or 20%, or 30%, or 40%, or 50% or 60%, or70%, or 80% or more. Compositions for suitable glass-based substratesare designed accordingly to comprise a desirable combination of: a glasstransition temperature (T_(g)), a liquid fragility index (m), andfictive temperature (T_(f)). In one or more embodiments, for an IOXtreatment temperature of less than or equal to 500° C., T_(g) is lessthan or equal to 650° C., a value of T_(f) minus T_(g) (e.g., thedifference between T_(f) and T_(g)) is greater than or equal to −30° C.,and m is greater than or equal to 25.

In one or more embodiments, the articles herein comprise a lithium-basedaluminosilicate composition and a fracture toughness that is greaterthan or equal to 0.75 MPa*m^(0.5). The stress profiles comprise: a spikeregion extending from the first surface to a knee; and a tail regionextending from the knee to a center of the glass-based article, the tailregion comprising: a negative curvature region wherein a secondderivative of stress as a function of depth is negative; the DOC beinggreater than or equal to 0.22 t, and a parabolic region originating atthe DOC and extending to the center of the glass-based article.

Under ideal conditions, shape and values of a stress profile in an ionexchanged glass are expected to obey a classic diffusion equation. Thesolution for this equation indicates that, in the case of a singleboundary through which the ions diffuse without limit, the stressprofile should be a complementary error function (erfc(x)). As usedherein, the terms “error function” and “erf” refer to the function thatis twice the integral of a normalized Gaussian function between 0 andx/σ√2. The terms “complementary error function” and “erfc” are equal toone minus the error function; i.e., erfc(x)=1−erf(x). For a boundedcase—e.g., where ions diffuse from opposite surfaces to the center ofthe glass—diffusion of strengthening cations follows a complementaryerror function until the ions meet at the center of the glass, afterwhich the whole diffusion profile may be better approximated by aparabolic shape profile for the ionic distribution. The stress profileis directly related to the ionic distribution inside the glass. Thestress profile should therefore be similar to the ionic distribution,regardless of whether the distribution of ions according to acomplementary error function or a parabolic function.

A divergence between expected and observed stress profiles may occur forcertain glasses. This is likely due to stress relaxation present in theglass and additional annealing effects. In the presence of stressrelaxation, an S-shape profile is achieved, which has a negativecurvature region wherein a second derivative of stress as a function ofdepth is negative. In the negative curvature region, the slope rate ofthe stress profile in the compressive layer between the surface and thedepth of compression (DOC) includes at least one region where the sloperate value changes sign, indicating that the slope (S) of the stressprofile is not a monotonically increasing or decreasing function.Instead, the slope (S) changes from a decreasing to an increasingpattern or vice-versa, thus defining a S-shaped region of the stressprofile.

The stress profiles herein have an S-shape before the DOC and aparabolic shape after the DOC. During an ion exchange (IOX) process,stress relaxation is occurring simultaneously while ions are diffusing.When diffusivity is fast, the amount of time at the IOX temperaturelimits stress relaxation to a very low level, and an almost lineardecaying profile going from a surface to a depth of the sample isexpected. A favorable glass composition would have a reasonably slowdiffusivity in order to enhance stress relaxation to achieve theprofiles herein. Slower diffusion, however, requires longer IOX times aswell as higher IOX temperatures. Time for IOX can be reduced when IOXtemperature increases. But, increased IOX temperatures can lead tohigher processing costs and possible release of undesirable oxide gases.An optimization between IOX temperature and diffusivity can be achievedin some glass compositions much easier than other glasses.

Generally, the stress profiles herein are not frangible, so a glasscomposition suitable for a high frangibility limit is desired.Accordingly, suitable glass compositions used herein have a fracturetoughness that is greater than or equal to 0.75 MPa*m^(0.5); preferablygreater than or equal to 0.8 MPa*m^(0.5); preferably greater than orequal to 0.85 MPa*m^(0.5). Specifically, suitable glass compositionsused herein have a fracture toughness as measured by the chevron notchedshort bar method that is greater than or equal to 0.75 MPa*m^(0.5);preferably greater than or equal to 0.8 MPa*m^(0.5); preferably greaterthan or equal to 0.85 MPa*m^(0.5). From a glass composition perspective,the presence of K₂O and P₂O₅ lowers the frangibility limit. In one ormore embodiments, a total of potassium oxide (K₂O) and phosphoruspentoxide (P₂O₅) in the glass composition is less than 2 mol % (e.g.,K₂O+P₂O₅<2 mol %.) Glass compositions containing Li₂O have higherfracture toughness relative to Na₂O only glasses. In one or moreembodiments, Li₂O content is greater than Na₂O. In other words, in oneor more embodiments, a molar ratio of sodium oxide (Na₂O) to lithiumoxide (Li₂O) is less than 1.0 at the center of the glass-based article.High fracture toughness may also correlate with improved damageresistance (lower damage depth for the same force).

The glass-based articles herein are advantageous in that they aredesigned to have excellent performance for deep damage and theirprofiles are non-frangible, by using stress where it is needed. Theprofiles herein are suitable for many glass styles, including 2.5Ddesigns where the glass thickness tapers to a much lower thickness onthe edges. Without intended to be bound by theory, it is understood thatby moving the tension away from the edge, through longer diffusiondurations, the performance of glass can be improved. The methodsdescribed herein are advantageous in that they feasible formanufacturing on a large scale using existing equipment and can be donein a reasonable timeframe. Use of longer diffusion durations herein areexpected to provide good performance in a 2.5D configuration.

Reference will now be made in detail to lithium aluminosilicate glassesaccording to various embodiments. Alkali aluminosilicate glasses havegood ion exchangeability, and chemical strengthening processes have beenused to achieve high strength and high toughness properties in alkalialuminosilicate glasses. Sodium aluminosilicate glasses are highly ionexchangeable glasses with high glass formability and quality. Lithiumaluminosilicate glasses are highly ion exchangeable glasses with highglass quality. The substitution of Al₂O₃ into the silicate glass networkincreases the interdiffusivity of monovalent cations during ionexchange. By chemical strengthening in a molten salt bath (e.g., KNO₃ orNaNO₃), glasses with high strength, high toughness, and high indentationcracking resistance can be achieved. The stress profiles achievedthrough chemical strengthening may have a variety of shapes thatincrease the drop performance, strength, toughness, and other attributesof the glass articles, as well as improved scratch resistance.

Therefore, lithium aluminosilicate glasses with good physicalproperties, chemical durability, and ion exchangeability have drawnattention for use as cover glass. Through different ion exchangeprocesses, greater central tension (CT), depth of compression (DOC), andcompressive stress (CS) can be achieved. The stress profiles describedherein provide increased drop performance for lithium containing glassarticles.

In embodiments of glass compositions described herein, the concentrationof constituent components (e.g., SiO₂, Al₂O₃, Li₂O, and the like) aregiven in mole percent (mol %) on an oxide basis, unless otherwisespecified. It should be understood that any of the variously recitedranges of one component may be individually combined with any of thevariously recited ranges for any other component.

Disclosed herein are ion exchange methods and stress profiles forlithium aluminosilicate glass compositions. The stress profiles exhibitscratch resistance. With reference to FIG. 1, the glass has a thicknesst and a first region under compressive stress (e.g., first and secondcompressive stress layers 120, 122 in FIG. 1) extending from the surfaceto a depth of compression (DOC) of the glass and a second region (e.g.,central region 130 in FIG. 1) under a tensile stress or central tension(CT) extending from the DOC into the central or interior region of theglass.

The compressive stress (CS) has a maximum or peak value, which typicallyoccurs at the surface of the glass (but such need not be the case as thepeak may occur at a depth from the surface of the glass), and the CSvaries with distance d from the surface according to a function.Referring again to FIG. 1, the first compressive stress layer 120extends from first surface 110 to a depth d₁ and the second compressivestress layer 122 extends from second surface 112 to a depth d₂.Together, these segments define a compression or CS of glass 100.

The compressive stress of both compressive stress layers (120, 122 inFIG. 1) is balanced by stored tension in the central region (130) of theglass.

FIG. 2 shows a schematic graph of a generalized stress profilecontaining a spike region near the surface extending to a knee, and atail region extending from the knee to deeper in the glass towards thecenter. Stress values are not absolute in this generalized graph, whichis denoted by the inclusion of “y” in the non-zero y-axis values. Thestress profile comprises: a compressive stress at the surface CS, adepth of layer (DOL_(sp)) of the spike region that is related to thediffusion depth of the ions near the spike, stress of the knee CS_(k),which is the stress at the asymptotic extrapolation of the spike anddeep profile regions, a depth of compression (DOC), which is thelocation where the stress is first zero inside the glass and changessign from compression to tension, and a central tension (CT) that is thestress at the center of the glass. In the spike region, there is anegative curvature region where a second derivative of stress as afunction of depth is negative. In FIG. 2, the convention is thatcompressive stress is positive and tension is negative for illustrationpurposes.

In one or more embodiments, the shape of the stress profile deeper thanthe DOC in the central tension (CT) region (where stress is in tension)may be approximated by an equation. In some embodiments, the stressprofile along the CT region may be approximated by equation (B):

Stress(x)=MaxCT−(((MaxCT·(n+1))/0.5^(n))·|(x/t)−0.5|^(n))  (B)

In equation (B), the stress (x) is the stress value at position x. Herethe stress is positive (tension). MaxCT is the maximum central tensionas a positive value in MPa. The value x is position along the thickness(t) in micrometers, with a range from 0 to t; x=0 is one surface (e.g.,110 in FIG. 1), x=0.5 t is the center of the glass-based article,stress(x)=MaxCT, and x=t is the opposite surface (e.g., 112 in FIG. 1).MaxCT used in equation (B) may be in the range from about 50 MPa toabout 350 MPa (e.g., 60 MPa to about 300 MPa, or from about 70 MPa toabout 270 MPa), and n is a fitting parameter from 1.5 to 5 (e.g., 2 to4, 2 to 3 or 1.8 to 2.2) whereby n=2 can provide a parabolic stressprofile, exponents that deviate from n=2 provide stress profiles withnear parabolic stress profiles. Reference herein to a “parabolic shape”profile includes profiles that fit both parabolic and near parabolicequations.

In the glass-based articles, there is an alkali metal oxide having anon-zero concentration that varies from one or both of first and secondsurfaces to a depth of layer (DOL) with respect to the metal oxide. Astress profile is generated due to the non-zero concentration of themetal oxide(s) that varies from the first surface. The non-zeroconcentration may vary along a portion of the article thickness. In someembodiments, the concentration of the alkali metal oxide is non-zero andvaries along a thickness range from about 0·t to about 0.3·t. In someembodiments, the concentration of the alkali metal oxide is non-zero andvaries along a thickness range from about 0·t to about 0.35·t, fromabout 0·t to about 0.4·t, from about 0·t to about 0.45·t, from about 0·tto about 0.48·t, or from about 0·t to about 0.50·t. The variation inconcentration may be continuous along the above-referenced thicknessranges. Variation in concentration may include a change in metal oxideconcentration of about 0.2 mol % or more along a thickness segment ofabout 100 micrometers. The change in metal oxide concentration may beabout 0.3 mol % or more, about 0.4 mol % or more, or about 0.5 mol % ormore along a thickness segment of about 100 micrometers. This change maybe measured by known methods in the art including microprobe.

In some embodiments, the variation in concentration may be continuousalong thickness segments in the range from about 10 micrometers to about30 micrometers. In some embodiments, the concentration of the alkalimetal oxide decreases from the first surface to a value between thefirst surface and the second surface and increases from the value to thesecond surface.

The concentration of alkali metal oxide may include more than one metaloxide (e.g., a combination of Na₂O and K₂O). In some embodiments, wheretwo metal oxides are utilized and where the radius of the ions differfrom one or another, the concentration of ions having a larger radius isgreater than the concentration of ions having a smaller radius atshallow depths, while at deeper depths, the concentration of ions havinga smaller radius is greater than the concentration of ions having alarger radius.

In one or more embodiments, the alkali metal oxide concentrationgradient extends through a substantial portion of the thickness t of thearticle. In some embodiments, the concentration of the metal oxide maybe about 0.5 mol % or greater (e.g., about 1 mol % or greater) along theentire thickness of the first and/or second section, and is greatest ata first surface and/or a second surface 0·t and decreases substantiallyconstantly to a value between the first and second surfaces. At thatvalue, the concentration of the metal oxide is the least along theentire thickness t; however the concentration is also non-zero at thatpoint. In other words, the non-zero concentration of that particularmetal oxide extends along a substantial portion of the thickness t (asdescribed herein) or the entire thickness t. The total concentration ofthe particular metal oxide in the glass-based article may be in therange from about 1 mol % to about 20 mol %.

The concentration of the alkali metal oxide may be determined from abaseline amount of the metal oxide in the glass-based substrate ionexchanged to form the glass-based article.

In one or more embodiments, the glass-based article comprises: alithium-based aluminosilicate composition. In one or more embodiments,the lithium-based aluminosilicate composition comprises potassium oxide(K₂O) and phosphorus pentoxide (P₂O₅) in an amount that is less than 2mol % of the composition, or less than 1.9 mol %, or less than 1.8 mol %of the composition, or less than 1.7 mol %, or less than 1.6 mol % ofthe composition, or less than 1.5 mol %, or less than 1.4 mol % of thecomposition, or less than 1.3 mol % of the composition, or less than 1.2mol % of the composition, or less than 1.1 mol %, or less than 1.0 mol %of the composition, or less than 0.9 mol %, or less than 0.8 mol % ofthe composition, or less than 0.7 mol %, or less than 0.6 mol % of thecomposition, or less than 0.5 mol % of the composition, and/or greaterthan or equal to 0.01 mol %, including all values and subrangestherebetween. In one or more embodiments, the lithium-basedaluminosilicate composition comprises potassium oxide (K₂O) andphosphorus pentoxide (P₂O₅) in a total amount of: greater than or equalto 0 mol % to less than 2 mol %, or greater than or equal to 0.01 mol %to less than 1.5 mol %, or greater than or equal to 0.5 mol % to lessthan 1 mol %, including all values and subranges therebetween.

In one or more embodiments, the lithium-based aluminosilicatecomposition comprises a lithium oxide (Li₂O) content of greater than 8mol %, or greater than 8.5 mol %, or greater than 9 mol %, or greaterthan 9.5 mol %, or greater than 10 mol %, or greater than or equal to10.5 mol %, or greater than or equal to 11 mol %, or greater than orequal to 11.5 mol %, or greater than or equal to 12 mol %, or greaterthan or equal to 12.5 mol %, or greater than or equal to 13 mol %, orgreater than or equal to 13.5 mol %, or greater than or equal to 14 mol%, or greater than or equal to 15 mol %, and/or less than or equal to 18mol %. In one or more embodiments, the lithium-based aluminosilicatecomposition comprises a lithium oxide (Li₂O) content of: greater than orequal to 8 mol % to less than or equal to 18 mol %, or greater than orequal to 9 mol % to less than or equal to 16 mol %, or greater than orequal to 10 mol % to less than or equal to 14 mol %, including allvalues and subranges therebetween.

In one or more embodiments, the composition at a center of theglass-based article comprises: 50 mol % to 69 mol % SiO₂; 12.5 mol % to25 mol % Al₂O₃; 0 mol % to 8 mol % B₂O₃; greater than 0 mol % to 4 mol %CaO; greater than 0 mol % to 17.5 mol % MgO; 0.5 mol % to 8 mol % Na₂O;0 mol % to 2.5 mol % La₂O₃; and greater than 8 mol % to 18 mol % Li₂O.The glass composition is characterized by a molar ratio of:(Li₂O+Na₂O+MgO)/Al₂O₃ from 0.9 to less than 1.3; andAl₂O₃+MgO+Li₂O+ZrO₂+La₂O₃+Y₂O₃ from greater than 23 mol % to less than50 mol %.

The glass-based articles disclosed herein comprise lithiumaluminosilicate glass compositions that exhibit a high fracturetoughness (K_(1C)). In some embodiments, the lithium aluminosilicateglass compositions are characterized by a K_(1C) fracture toughnessvalue as measured by a chevron short bar (CNSB) method of at least 0.75MPa*m^(0.5).

In some embodiments, the glass compositions exhibit a K_(1C) valuemeasured by CNSB method of at least 0.75, such as at least 0.76, atleast 0.77, at least 0.78, at least 0.79, at least 0.80, at least 0.81,at least 0.82, at least 0.83, at least 0.84, at least 0.85, at least0.86, at least 0.87, at least 0.88, at least 0.89, at least 0.90, atleast 0.91, at least 0.92, at least 0.93 at least 0.94, at least 0.95,or at least 0.96. In embodiments, the glass compositions exhibit aK_(1C) value measured by CNSB method from greater than or equal to 0.75to less than or equal to 1.00, such as from greater than or equal to0.76 to less than or equal to 0.99, from greater than or equal to 0.77to less than or equal to 0.98, from greater than or equal to 0.78 toless than or equal to 0.97, from greater than or equal to 0.79 to lessthan or equal to 0.96, from greater than or equal to 0.80 to less thanor equal to 0.95, from greater than or equal to 0.81 to less than orequal to 0.94, from greater than or equal to 0.82 to less than or equalto 0.93, from greater than or equal to 0.83 to less than or equal to0.92, from greater than or equal to 0.84 to less than or equal to 0.91,from greater than or equal to 0.85 to less than or equal to 0.90, fromgreater than or equal to 0.86 to less than or equal to 0.89, or fromgreater than or equal to 0.87 to less than or equal to 0.88, and allranges and sub-ranges between the foregoing values.

In one or more embodiments, the composition at the center of theglass-based article comprises: a molar ratio of sodium dioxide (Na₂O) tolithium dioxide (Li₂O) of less than 1.0 and/or greater than or equal to0.1, including less than or equal to 0.99, or less than or equal to 0.9,or less than or equal to 0.85, or less than or equal to 0.8, or lessthan or equal to 0.75, or less than or equal to 0.7, or less than orequal to 0.65, or less than or equal to 0.63, or less than or equal to0.6, or less than or equal to 0.55, or less than or equal to 0.5, orless than or equal to 0.45, or less than or equal to 0.4, or less thanor equal to 0.35, or less than or equal to 0.3, or less than or equal to0.25, or less than or equal to 0.2, or less than or equal to 0.15, andall values and subranges therebetween. In one or more embodiments, thecomposition at the center of the glass-based article comprises: a molarratio of sodium dioxide (Na₂O) to lithium dioxide (Li₂O) of: greaterthan or equal to 0.1 to less than 1.0, or greater than or equal to 0.15to less than or equal to 0.9, or greater than or equal to 0.2 to lessthan or equal to 0.85, and all values and subranges therebetween.

In one or more embodiments, the glass-based article comprises: a depthof compression (DOC) that is greater than or equal to 0.22 t, or greaterthan or equal to 0.225 t, or greater than or equal to 0.23 t, or greaterthan or equal to 0.235 t, or greater than or equal to 0.24 t, or greaterthan or equal to 0.245 t, or greater than or equal to 0.25 t, and/orless than or equal to 0.30 t, or less than or equal to 0.29 t, or lessthan or equal to 0.28 t, or less than or equal to 0.27 t, or less thanor equal to 0.26 t, including all values and subranges therebetween. Inone or more embodiments, the glass-based article comprises: a depth ofcompression (DOC) that is greater than or equal to 0.22 t and less thanor equal to 0.30 t, or greater than or equal to 0.225 t and less than orequal to 0.29 t, or greater than or equal to 0.23 t and less than orequal to 0.8 t, including all values and subranges therebetween.

In one or more embodiments, the glass-based article comprises: a depthof compression (DOC) that is greater than or equal to 150 micrometers,or greater than or equal to 155 micrometers, or greater than or equal to160 micrometers, or greater than or equal to 165 micrometers, or greaterthan or equal to 170 micrometers, including all values and subrangestherebetween.

In one or more embodiments, the glass-based article comprises: t isgreater than or equal to 0.02 mm and/or is less than or equal to 2 mm,including t is less than or equal to 1 mm, or less than or equal to 0.8mm, or less than or equal to 0.75 mm, or less than or equal to 0.73 mm,or less than or equal to 0.70 mm, or less than or equal to 0.65 mm, orless than or equal to 0.6 mm, or less than or equal to 0.55 mm, and/orgreater than or equal to 0.1 mm, or greater than or equal to 0.5 mm,including all values and subranges therebetween. In one or moreembodiments, the glass-based article comprises: t is greater than orequal to 0.02 mm and is less than or equal to 2 mm, or greater than orequal to 0.55 mm and is less than or equal to 1 mm, or greater than orequal to 0.7 mm and is less than or equal to 0.8 mm, including allvalues and subranges therebetween.

Desirable values of maximum compressive stress (CS_(max)) are related toan application for the glass-based articles. Conditions of IOX is afactor that effects CS_(max). In some embodiments, a spike is introducedto increase the CS_(max). In some embodiments, a spike is notintroduced. In one or more embodiments, regardless of IOX conditions,the glass-based article comprises: a maximum compressive stress(CS_(max)) that is greater than or equal to 150 MPa, greater than orequal to 300 MPa, greater than or equal to 350 MPa, greater than orequal to 400 MPa, greater than or equal to 450 MPa, greater than orequal to 500 MPa, greater than or equal to 550 MPa, greater than orequal to 600 MPa, greater than or equal to 650 MPa, greater than orequal to 700 MPa, greater than or equal to 750 MPa, greater than orequal to 800 MPa, greater than or equal to 850 MPa, greater than orequal to 900 MPa, greater than or equal to 950 MPa, greater than orequal to 1000 MPa, greater than or equal to 1050 MPa, greater than orequal to 1100 MPa, greater than or equal to 1150 MPa, or greater than orequal to 1200 MPa, including all values and subranges therebetween. Inone or more embodiments, the glass-based article comprises: a maximumcompressive stress (CS_(max)) of: greater than or equal to 150 MPa andless than or equal to 1200 MPa, greater than or equal to 250 MPa andless than or equal to 1100 MPa, greater than or equal to 350 MPa andless than or equal to 1000 MPa, including all values and subrangestherebetween.

In one or more embodiments, the negative curvature region comprises anaverage compressive stress (CS) of greater than or equal to 50 MPa toless than or equal to 120 MPa, or greater than or equal to 55 MPa toless than or equal to 115 MPa, or greater than or equal to 60 MPa toless than or equal to 110 MPa, including all values and subrangestherebetween.

In one or more embodiments, a peak central tension (CT) in the parabolicregion in the range of greater than or equal to 100 MPa to less than orequal to 200 MPa, or greater than or equal to 125 MPa to less than orequal to 175 MPa, including all values and subranges therebetween.

In one or more embodiments, a value of a peak central tension(CT)*thickness (t) in the parabolic region is in the range of greaterthan or equal to 80 MPa to less than or equal to 160 MPa, or greaterthan or equal to 90 MPa to less than or equal to 155 MPa, including allvalues and subranges therebetween.

In one or more embodiments, the glass-based articles comprise a retainedstrength of greater than or equal to 170 MPa as measured for an articlehaving a thickness of 600.0 μm after impact with 30 grit sandpaper witha force of 470.0 N. In one or more embodiments, the glass-based articlescomprise a retained strength of greater than or equal to 170 MPa asmeasured for an article having a thickness of 600.0 μm after impact with80 grit sandpaper with a force of 470.0 N. In one or more embodiments,the glass-based articles comprise a first retained strength of greaterthan or equal to 170 MPa as measured for an article having a thicknessof 600.0 μm after impact with 30 grit sandpaper with a force of 470.0 N,and a second retained strength of greater than or equal to 170 MPa asmeasured for an article having a thickness of 600.0 μm after impact with80 grit sandpaper with a force of 470.0 N. In one or more embodiments,first retained strength and the second retained strength are ±5 MPa.

In one or more embodiments, the glass-based articles comprise, asmeasured for an article having a thickness of 600.0 μm after impact with30 grit sandpaper with a force of 470.0 N: a retained strength ofgreater than or equal to 170 MPa to less than or equal to 200 MPa, orgreater than or equal to 175 MPa to less than or equal to 195 MPa, orgreater than or equal to 180 MPa to less than or equal to 190 MPa,including all values and subranges therebetween.

In one or more embodiments, the glass-based articles comprise, asmeasured for an article having a thickness of 600.0 μm after impact with80 grit sandpaper with a force of 470.0 N: a retained strength ofgreater than or equal to 170 MPa to less than or equal to 200 MPa, orgreater than or equal to 175 MPa to less than or equal to 195 MPa, orgreater than or equal to 180 MPa to less than or equal to 190 MPa,including all values and subranges therebetween.

In one or more embodiments, the glass-based articles comprise, asmeasured for an article having a thickness of 600.0 μm after impact with30 grit sandpaper with a force of 470.0 N and as measured independentlyfor an article after impact with 80 grit sandpaper with a force of 470.0N: a retained strength of greater than or equal to 170 MPa to less thanor equal to 200 MPa, or greater than or equal to 175 MPa to less than orequal to 195 MPa, or greater than or equal to 180 MPa to less than orequal to 190 MPa, including all values and subranges therebetween.

Design of Glass-Based Substrates

In one or more embodiments, the glass stress-based substrates achieve astress relaxation rate, which is (100*(1−ratio of relaxed stress (σ_(r))to initial stress (σ_(o))) of greater than or equal to 10%, or 20%, or30%, or 40%, or 50% or 60%, or 70%, or 80%, or more and/or less than orequal to 100%, less than or equal to 90%, less than or equal to 85%,including all values and subranges therebetween. In one or moreembodiments, the stress relaxation rate of the glass stress-basedsubstrates is: greater than or equal to 10% and less than or equal to100%, greater than or equal to 20% and less than or equal to 90%,greater than or equal to 25% and less than or equal to 80%, includingall values and subranges therebetween. Compositions for suitableglass-based substrates are designed accordingly to comprise a desirablecombination of: a glass transition temperature (T_(g)), a liquidfragility index (m), and fictive temperature (T_(f)).

In one or more embodiments, the T_(g) is greater than or equal to 550°C. or less than or equal to 650° C., including all values and subrangestherebetween. In one or more embodiments, the T_(g) is greater than orequal to 550° C. and less than or equal to 650° C., including all valuesand subranges therebetween.

In one or more embodiments, the value of T_(f) minus T_(g) is greaterthan or equal to −30° C. or less than or equal to 100° C., including allvalues and subranges therebetween. In one or more embodiments, the valueof T_(f) minus T_(g) is greater than or equal to −30° C. and less thanor equal to 100° C., or greater than or equal to 0° C. and less than orequal to 95° C., or greater than or equal to 30° C. and less than orequal to 90° C., including all values and subranges therebetween.

In one or more embodiments, m is greater than or equal to 25 or lessthan or equal to 60, including all values and subranges therebetween. Inone or more embodiments, m is greater than or equal to 25 and less thanor equal to 60, or greater than or equal to 30 and less than or equal to55, greater than or equal to 35 and less than or equal to 50, includingall values and subranges therebetween.

Viscosity of the glass-based substrate contributes to stress relaxationrate. For a glass being at its nonequilibrium state, viscosity isextremely high for measurement. A desired ion exchange (IOX) treatmenttemperature (T_(IOX)) and a glass transition temperature are preferredto have the following range: T_(g)−200° C.<T_(IOX)<T_(g)−50° C. Theupper limit is established to make sure there is still retained ionexchange stress rather than all stress that is mostly relaxed.

Stress relaxation is a common phenomenon for glass under stress.Wherever there is stress, glass undergoes stress relaxation. Stressrelaxation follows stretched exponential equation as shown in equation(1).

$\begin{matrix}{\sigma_{r} = {\sigma_{0}\left\{ {1 - {\exp\left\lbrack {- \left( \frac{t}{r} \right)^{\beta}} \right\rbrack}} \right\}}} & (1)\end{matrix}$

where σ_(r) is the relaxed stress, σ₀ is the initial stress, t is thephysical time, and τ is the characteristic relaxation time, β is thestretched exponential. Stress relaxation according to equation (1) is aproperty of a base glass substrate, used without requiring subjectingthe substrate to ion exchange (IOX). The expectation is if a glassundergoes significant stress relaxation in thermal conditions normallyused for IOX, then a glass article having undergone IOX under suchthermal conditions will also experience significant stress relaxation.Therefore, stress relaxation according to equation (1) is a way topredict stress relaxation performance on IOX'd glass. In a typical IOXtemperature range, the relaxation time can be approximated by theArrhenius equation (2):

$\begin{matrix}{\tau = {\tau_{0}{\exp\left( \frac{E}{RT} \right)}}} & (2)\end{matrix}$

where τ₀ is the relaxation time when temp T goes to infinity, E isactivation energy.

Relaxation time is directly linked to viscosity through Maxwell equation(3):

$\begin{matrix}{\tau = \frac{\eta}{G}} & (3)\end{matrix}$

where η is viscosity and G is shear modulus. Based on lab stressrelaxation data, the shear modulus is different from the lab measuredshear modulus. The article entitled “Topological origin of stretchedexponential relaxation in glass” by Potuzak et. al [Marcel Potuzak,Roger C. Welch, and John C. Mauro, J. of Chem. Phys. 135, 214502(2011)]discusses stress relaxation measurement and is incorporatedherein by reference. To best fit lab measured stress relaxation, G isapproximately 100 MPa.

According to MAP non-equilibrium viscosity model by Mauro et al [J. C.Mauro, D. C. Allan, M. Potuzak, Phys. Rev. B 80, 094204 (2009).] andcomposition dependent viscosity model [X. J. Guo, J. C. Mauro, D. C.Allan, M. M. Smedskjaer, J. Am. Ceram. Soc. 2018; 101:1169-1179], theexpression to determine the composition dependence of nonequilibriumglass viscosity is:

log₁₀ η(T,T _(f) ,x)=y(T,T _(f) ,x)log₁₀ η_(eq)(T _(f) ,x)+└(1−y(T,T_(f) ,x)┘log₁₀ η_(ne)(T,T _(f) ,x),   (4)

where

$\begin{matrix}{{{y\left( {T,T_{f},x} \right)} = \left\lbrack \frac{\min\left( {T,T_{f}} \right)}{\max\left( {T,T_{f}} \right)} \right\rbrack^{{p{(x_{ref})}}{{m{(x)}}/{m{(x_{ref})}}}}},} & (5)\end{matrix}$

In the viscosity model of Eq. (4), η_(eq) and η_(ne) are given by Eqs.(6) and (7), respectively. We assume that A(x)=A(x_(ref)) andΔH(x)=ΔH(x_(ref)) are constant over the composition range of interest,i.e., the composition dependence of η_(ne)(T,T_(f),x) is contained inthe last term of Eq. (7).

$\begin{matrix}{{{\log_{10}{\eta_{eq}\left( T_{f} \right)}} = {{\log_{10}\eta_{\infty}} + {\left( {12 - {\log_{10}\eta_{\infty}}} \right)\frac{T_{g}}{T_{f}}{\exp\left\lbrack {\left( {\frac{m}{12 - {\log_{10}\eta_{\infty}}} - 1} \right)\left( {\frac{T_{g}}{T_{f}} - 1} \right)} \right\rbrack}}}},} & (6)\end{matrix}$

where T_(g) is the glass transition temperature (10¹² Pa s isokomtemperature), m is the liquid fragility index:

m(x)=∂ log 10 ηeq(T,x)∂(T _(g)(x)/T)□T=T _(g)(x)

and η_(∞)=10^(−2.9) Pa·s is the infinite temperature limit of liquidviscosity, which is a universal composition independent constant forsilicate liquids.

$\begin{matrix}{{\log_{10}{\eta_{ne}\left( {T,T_{f}} \right)}} = {A + \frac{\Delta H}{{kT}{ln10}} - {\frac{S_{\infty}}{k{ln10}}{{\exp\left\lbrack {{- \frac{T_{g}}{T_{f}}}\left( {\frac{m}{12 - {\log_{10}\eta_{\infty}}} - 1} \right)} \right\rbrack}.}}}} & (7)\end{matrix}$

where A is a constant related to the attempt frequency, ΔH the dominantactivation enthalpy for isostructural flow, and S_(∞) is theconfigurational entropy in the infinite temperature limit.

Based on previous enthalpy landscape modeling of Mauro, an exponentiallylarge number of configurational microstates exists for higher fragilitysystems, each with an exponentially large number of possible transitionstates. Hence, we assume that S_(∞) varies exponentially with fragility,

$\begin{matrix}{{S_{\infty}(x)} = {{S_{\infty}\left( x_{ref} \right)}{{\exp\left( \frac{{m(x)} - {m\left( x_{ref} \right)}}{12 - {\log_{10}\eta_{\infty}}} \right)}.}}} & (7)\end{matrix}$

Examples herein demonstrate the use of this model.

In one or more embodiments, a method of manufacturing a glass-basedarticle comprises: preparing a glass composition; exposing the glasscomposition to a process to form a glass-based substrate comprising: aglass transition temperature (T_(g)), a liquid fragility index (m), andfictive temperature (T_(f)), wherein T_(g) is less than or equal to 650°C., the difference between T_(f) and T_(g) is greater than or equal to−30° C., and m is greater than or equal to 25; and exposing theglass-based substrate to ion exchange conditions of less than or equalto 550° C., including less than or equal to 500° C., to form aglass-based article such that a stress relaxation rate is greater thanor equal to 10%.

Glass-Based Substrates

Examples of materials that may be used to form the glass-basedsubstrates include glass and glass-ceramic materials. Exemplary glassesthat may be used as substrates may include alkali-alumino silicate glasscompositions or alkali-containing aluminoborosilicate glasscompositions, though other glass compositions are contemplated. Specificexamples of glass-based substrates that may be used include but are notlimited to an alkali-alumino silicate glass, an alkali-containingborosilicate glass, an alkali-alumino borosilicate glass, analkali-containing lithium alumino silicate glass, or analkali-containing phosphate glass. The glass-based substrates have basecompositions that may be characterized as ion exchangeable. As usedherein, “ion exchangeable” means that a substrate comprising thecomposition is capable of exchanging cations located at or near thesurface of the substrate with cations of the same valence that areeither larger or smaller in size.

In one or more embodiments, glass-based substrates may include alithium-containing aluminosilicate.

In embodiments, the glass-based substrates may be formed from anycomposition capable of forming the stress profiles. In some embodiments,the glass-based substrates may be formed from the glass compositionsdescribed in U.S. application Ser. No. 16/202,691 titled “Glasses withLow Excess Modifier Content,” filed Nov. 28, 2018, the entirety of whichis incorporated herein by reference. In some embodiments, the glassarticles may be formed from the glass compositions described in U.S.application Ser. No. 16/202,767 titled “Ion-Exchangeable Mixed AlkaliAluminosilicate Glasses,” filed Nov. 28, 2018, the entirety of which isincorporated herein by reference.

The glass-based substrates may be characterized by the manner in whichit may be formed. For instance, the glass-based substrates may becharacterized as float-formable (i.e., formed by a float process),down-drawable and, in particular, fusion-formable or slot-drawable(i.e., formed by a down draw process such as a fusion draw process or aslot draw process). In embodiments, the glass-based substrates may beroll formed. For glass-ceramics, a ceramming step may be included. Otherforming methods may be used for glasses and glass-ceramics.

Some embodiments of the glass-based substrates described herein may beformed by a down-draw process. Down-draw processes produce glass-basedsubstrates having a uniform thickness that possess relatively pristinesurfaces. Because the average flexural strength of the glass article iscontrolled by the amount and size of surface flaws, a pristine surfacethat has had minimal contact has a higher initial strength. In addition,down drawn glass articles have a very flat, smooth surface that can beused in its final application without costly grinding and polishing.

Some embodiments of the glass-based substrates may be described asfusion-formable (i.e., formable using a fusion draw process). The fusionprocess uses a drawing tank that has a channel for accepting moltenglass raw material. The channel has weirs that are open at the top alongthe length of the channel on both sides of the channel. When the channelfills with molten material, the molten glass overflows the weirs. Due togravity, the molten glass flows down the outside surfaces of the drawingtank as two flowing glass films. These outside surfaces of the drawingtank extend down and inwardly so that they join at an edge below thedrawing tank. The two flowing glass films join at this edge to fuse andform a single flowing glass article. The fusion draw method offers theadvantage that, because the two glass films flowing over the channelfuse together, neither of the outside surfaces of the resulting glassarticle comes in contact with any part of the apparatus. Thus, thesurface properties of the fusion drawn glass article are not affected bysuch contact.

Some embodiments of the glass-based substrates described herein may beformed by a slot draw process. The slot draw process is distinct fromthe fusion draw method. In slot draw processes, the molten raw materialglass is provided to a drawing tank. The bottom of the drawing tank hasan open slot with a nozzle that extends the length of the slot. Themolten glass flows through the slot/nozzle and is drawn downward as acontinuous glass article and into an annealing region.

In one or more embodiments, a base composition comprises: 50 mol % to 69mol % SiO₂; 12.5 mol % to 25 mol % Al₂O₃; 0 mol % to 8 mol % B₂O₃;greater than 0 mol % to 4 mol % CaO; greater than 0 mol % to 17.5 mol %MgO; 0.5 mol % to 8 mol % Na₂O; 0 mol % to 2.5 mol % La₂O₃; and greaterthan 8 mol % to 18 mol % Li₂O. The glass composition is characterized by(Li₂O+Na₂O+MgO)/Al₂O₃ from 0.9 to less than 1.3; andAl₂O₃+MgO+Li₂O+ZrO₂+La₂O₃+Y₂O₃ from greater than 23 mol % to less than50 mol %.

In one or more embodiments, the glass-based substrates described hereinmay exhibit an amorphous microstructure and may be substantially free ofcrystals or crystallites. In other words, the glass-base substratesarticles exclude glass-ceramic materials in some embodiments.

In one or more embodiments, an annealing step is conducted after ionexchange. That is, the annealing step is optional. Annealing attemperatures of, for example, 500° C.±50° C. for durations ofapproximately 15 to 60 minutes may be used to achieve deeper depth ofcompression (DOC) and/or stress relaxation rate.

Ion Exchange (IOX) Treatment

Chemical strengthening of glass-based substrates having basecompositions is done by placing the ion-exchangeable glass-basedsubstrates to an ion exchange medium. In embodiments, the ion exchangemedium may be a molten bath containing cations (e.g., K+, Na+, Ag+, etc)that diffuse into the glass while the smaller alkali ions (e.g., Na+,Li+) of the glass diffuse out into the molten bath. The replacement ofthe smaller cations by larger ones creates compressive stresses near thesurface of glass. Tensile stresses are generated in the interior of theglass to balance the near-surface compressive stresses.

With respect to ion exchange processes, they may independently be athermal-diffusion process or an electro-diffusion process. Non-limitingexamples of ion exchange processes in which glass is immersed inmultiple ion exchange baths, with washing and/or annealing steps betweenimmersions, are described in U.S. Pat. No. 8,561,429, by Douglas C.Allan et al., issued on Oct. 22, 2013, entitled “Glass with CompressiveSurface for Consumer Applications,” and claiming priority from U.S.Provisional Patent Application No. 61/079,995, filed Jul. 11, 2008, inwhich glass is strengthened by immersion in multiple, successive, ionexchange treatments in salt baths of different concentrations; and U.S.Pat. No. 8,312,739, by Christopher M. Lee et al., issued on Nov. 20,2012, and entitled “Dual Stage Ion Exchange for Chemical Strengtheningof Glass,” and claiming priority from U.S. Provisional PatentApplication No. 61/084,398, filed Jul. 29, 2008, in which glass isstrengthened by ion exchange in a first bath is diluted with an effluention, followed by immersion in a second bath having a smallerconcentration of the effluent ion than the first bath. The contents ofU.S. Pat. Nos. 8,561,429 and 8,312,739 are incorporated herein byreference in their entireties.

After an ion exchange process is performed, it should be understood thata composition at the surface of a glass article may be different thanthe composition of the as-formed glass-based substrate (i.e., theglass-based substrate before it undergoes an ion exchange process). Thisresults from one type of alkali metal ion in the as-formed glass, suchas, for example Li⁺ or Na⁺, being replaced with larger alkali metalions, such as, for example Na⁺ or K⁺, respectively. However, the glasscomposition at or near the center of the depth of the glass articlewill, in embodiments, still have the composition of the as-formedglass-based substrate.

In one or more embodiments, the potassium salt comprises: KNO₃, K₂CO₃,K₃PO₄, K₂SO₄, K₃BO₃, KCl, or combinations thereof.

In one or more embodiments, the sodium salt comprises: NaNO₃, Na₂CO₃,Na₃PO₄, Na₂SO₄, Na₃BO₃, NaCl, or combinations thereof.

In one or more embodiments, the lithium salt comprises: LiNO₃, Li₂CO₃,Li₃PO₄, Li₂SO₄, Li₃BO₃, LiCl, or combinations thereof.

In one or more embodiments, the potassium salt comprises KNO₃, thesodium salt comprises NaNO₃, and the lithium salt comprises LiNO₃.

After IOX treatment, an optional annealing step may be applied asdiscussed above.

In one or more embodiments, a method of manufacturing a glass-basedarticle comprises: exposing a glass-based substrate having opposingfirst and second surfaces defining a substrate thickness (t) and alithium-based aluminosilicate composition to an ion exchange treatmentcomprising: a first molten salt bath and a second molten salt bath toform the glass-based article; wherein the glass-based article comprises:a fracture toughness that is greater than or equal to 0.75 MPa*m^(0.5);and a stress profile comprising: a spike region extending from the firstsurface to a knee; and a tail region extending from the knee to a centerof the glass-based article, the tail region comprising: a negativecurvature region wherein a second derivative of stress as a function ofdepth is negative; a depth of compression (DOC) that is greater than orequal to 0.22 t, and a parabolic region originating at the DOC andextending to the center of the glass-based article.

End Products

The glass-based articles disclosed herein may be incorporated intoanother article such as an article with a display (or display articles)(e.g., consumer electronics, including mobile phones, tablets,computers, navigation systems, and the like), architectural articles,transportation articles (e.g., automobiles, trains, aircraft, sea craft,etc.), appliance articles, or any article that requires sometransparency, scratch-resistance, abrasion resistance or a combinationthereof. An exemplary article incorporating any of the glass articlesdisclosed herein is shown in FIGS. 3A and 3B. Specifically, FIGS. 3A and3B show a consumer electronic device 200 including a housing 202 havingfront 204, back 206, and side surfaces 208; electrical components (notshown) that are at least partially inside or entirely within the housingand including at least a controller, a memory, and a display 210 at oradjacent to the front surface of the housing; and a cover 212 at or overthe front surface of the housing such that it is over the display. Insome embodiments, at least a portion of at least one of the cover 212and/or housing 202 may include any of the glass articles disclosedherein.

EXAMPLES

Various embodiments will be further clarified by the following examples.In the Examples, prior to being strengthened, the Examples are referredto as “substrates”. After being subjected to strengthening, the Examplesare referred to as “articles” or “glass-based articles”.

In the following examples, glass substrates according to Compositions Aor B were ion exchanged and the resulting articles tested. CompositionsA and B and glass substrates resulting therefrom had the followingattributes.

Composition A: 17.83 mol % Al₂O₃, 6.11 mol % B₂O₃, 4.41 mol % MgO, 1.73mol % Na₂O, 58.39 mol % SiO₂, 0.08 mol % SnO₂, 0.18 mol % K₂O, 0.02 mol% Fe₂O₃, 0.58 mol % CaO, and 10.66 mol % Li₂O (0.00 mol % SrO, 0.00 mol% ZnO, and 0.00 mol % P₂O₅); and a Na₂O/Li₂O molar ratio of 0.16. Theglass substrate according to Composition A had: a fracture toughness of0.85 mPa MPa*m^(0.5); a T_(f) of about 660° C., a T_(g) of about 617°C., a difference between T_(f) and T_(g) of about 43° C.; and a liquidfragility index (m) of 35.

Composition B: 12.88 mol % Al₂O₃, 1.84 mol % B₂O₃, 2.86 mol % MgO, 2.39mol % Na₂O, 70.96 mol % SiO₂, 0.07 mol % SnO₂, 0.02 mol % Fe₂O₃, 8.13mol % Li₂O, and 0.85 mol % ZnO, (0.00 mol % K₂O, 0.00 mol % CaO, 0.00mol % SrO, and 0.00 mol % P₂O₅); and a Na₂O/Li₂O molar ratio of 0.29.The glass substrate according to Composition B had a fracture toughnessof 0.8 mPa MPa*m^(0.5).

The stress profiles of experimental examples herein were measured viathe Refractive Near Field (RNF) method where the CT matches themeasurements of CT provided by scattering polarimetry using a SCALP-5made by Glasstress Co., Estonia. In addition, due to limitations of theRNF to provide accurate information in the first −2 μm of the stressprofile due to the size of the beam used in this measurement technique,the RNF data is extrapolated to the surface to find the stress at thesurface so that it also matches the measurements done by the FSM-6000 LEfrom Orihara, Japan that measures the estimated stress at the surface.Therefore, the total stress profile matches at the center of the samplethe CT measured by the SCALP instrument and at the surface the CSmeasured by the FSM-6000 LE instrument, using a light source at 365 nm,providing an accurate representation of the whole stress profile fromsurface to the center of the sample.

The term “retained strength,” as used herein, refers to the strength ofa glass article after damage introduction by an impact force when thearticle is bent to impart tensile tress. Damage is introduced accordingto a “surface impact test” method described in U.S. Patent PublicationNo. 2019/0072469 A1, which is incorporated herein by reference. Forexample, an apparatus for impact testing a glass article is shown asreference number 1100 in FIG. 10. The apparatus 1100 includes a pendulum1102 including a bob 1104 attached to a pivot 1106. The term “bob” on apendulum, as used herein, is a weight suspended from and connected to apivot by an arm. Thus, the bob 1104 shown is connected to the pivot 1106by an arm 1108. The bob 1104 includes a base 1110 for receiving a glassarticle, and the glass article is affixed to the base. The apparatus1100 further includes an impacting object 1140 positioned such that whenthe bob 1104 is released from a position at an angle greater than zerofrom the equilibrium position, the surface of the bob 1104 contacts theimpacting object 1140. The impacting object includes an abrasive sheethaving an abrasive surface to be placed in contact with the outersurface of the glass article. The abrasive sheet may comprise sandpaper,which may have a grit size in the range of 30 grit to 400 grit, or 100grit to 300 grit, for example 30 or 80 grit.

For purposes of this disclosure, the impacting object was in the form ofa 6 mm diameter disk of 30 grit or 80 grit sandpaper affixed to theapparatus. A glass article having a thickness of approximately 600.0 μmwas affixed to the bob. For each impact, a fresh sandpaper disk wasused. Damage on the glass article was done at approximately 470 N impactforce by pulling the swing of the arm of the apparatus to approximatelya 90° angle. Approximately 10 samples of each glass article wereimpacted.

After twelve hours or more of the damage introduction, the glassarticles were fractured in four-point bending (4PB). The damaged glassarticle was placed on support rods (support span) with the damaged siteon the bottom (i.e., on the tension side) and between the load roads(loading span). For purposes of this disclosure, the loading span was 18mm and the support span was 36 mm. The radius of curvature of load andsupport rods was 3.2 mm. Loading was done at a constant displacementrate of 5 mm/min using a screw-driven testing machine (Instron®,Norwood, Mass., USA) until failure of glass. 4PB tests were done at atemperature of 22° C.±2° C. and at a RH (relative humidity) of 50%±5%.

The applied fracture stress (or the applied stress to failure) σ_(app)in four-point bending (4PB) was calculated from the equation (C)

$\begin{matrix}{\sigma_{app} = {\frac{1}{\left( {1 - v^{2}} \right)}\frac{3{P\left( {L - a} \right)}}{2{bh}^{2}}}} & (C)\end{matrix}$

where, P is the maximum load to failure, L (=36 mm) is the distancebetween support rods (support span), a (=18 mm) is the distance betweenthe loading rods (loading span), b is the width of the glass plate, h isthe thickness of the glass plate and v is the Poisson's Ratio of theglass composition. The term (1/(1−v²)) in Eq. (C) considers thestiffening effect of a plate. In four-point bending, stress is constantunder the loading span and thus, the damaged site is under mode Iuniaxial tensile stress loading. The stressing rate of the 4-point bendtesting for the specimens was estimated to be between 15 to 17 MPa persec. The retained strength of the glass composition is the highestapplied fracture stress at which failure does not occur.

Examples 1-2 and A-B (Comparative)

Table 1 provides a summary of dual ion exchange (DIOX) conditions usingnitrate salts of potassium (K) and sodium (Na), as noted, for Examples1-2. A substrate according to composition A having a thickness of 800micrometers was used. The DIOX conditions included a preheat at 380° C.for 10 minutes and were the same for both Examples 1-2. Also shown inTable 1 is data for: percentage weight gain, compressive stress (CS),knee depth of layer (DOL_(k)), and central tension (CT). Both Step I andStep II included the addition of 0.5 wt. % silicic acid to the IOX bath.Between Step I and Step II, the substrate was cleaned to remove excesssalt.

TABLE 1 Weight DIOX Gain CS DOL_(k) CT EXAMPLE Substrate Step I* StepII* (%) (MPa) (μm) (MPa) 1 A 60 wt % K/ 100 wt % K 0.0596 894.4 6.79149.5 40 wt % Na, 500° C., 450° C., 45 minutes 10 hours 2 A 60 wt % K/100 wt % K 0.0555 — — — 40 wt % Na, 500° C., 450° C., 45 minutes 10hours *Each of Step I and Step II included the addition of 0.5 wt. %silicic acid.

Examples 1-2 were annealed at 500° C. after DIOX. Table 2 provides theCT data and DOC (μm).

TABLE 2 Annealing time CT DOC EXAMPLE (minutes) (MPa) (μm) 1 30 125 2100.2625 · t 2 60 105 220 0.275 t

Table 3 provides a summary of single ion exchange (SIOX) conditionsusing nitrate salts of potassium (K), sodium (Na), and lithium (Li) asnoted, for Examples A-B (comparative). Example A used an 800micrometer-thick substrate of Composition A. Example B used an 800micrometer-thick substrate of Composition B. Also shown in Table 3 isdata for: compressive stress (CS), compressive stress at a knee(CS_(k)), knee depth of layer (DOL_(k)), central tension (CT), and depthof compression (DOC) values. The IOX step included the addition of 0.5wt. % silicic acid to the IOX bath.

TABLE 3 EX- Sub- CS DOL_(k) CT DOC AMPLE strate SIOX* (MPa) (μm) (MPa)(μm) A A 90 wt % K/ 600 5 110 167 10 wt % Na,/ 0.209 t 1.4 Li 450° C.,8.4 hours B B 93.5 wt % K/ 700 7 88 180 6.5 wt % Na, 0.225 t 430° C.,4.5 hours *included the addition of 0.5 wt. % silicic acid.

FIG. 4 provides stress profiles (stress (MPa) versus depth(micrometers)) for Examples 1-2 and A-B (comparative). FIG. 4 showsregions of negative curvature: for Example 1 the region of negativecurvature includes depths of approximately 20 to approximately 140micrometers and for Example 2 the region of negative curvature includesdepths of approximately 10 to approximately 160 micrometers. FIG. 5 is aplot of a sodium dioxide (Na₂O) concentration versus depth for Example 1as measured by GD-OES. Solid line is a linear fit of the Na₂O profile.Surface CS as a result of force balance is equal to CS=BEΔC/(1−v), whereΔC=C₀−C_(ave) surface Na₂O concentration subtract the average Na₂Oconcentration through thickness, B is linear lattice dilationcoefficient, E is Young's modulus, v is Poisson's ratio. Based on FIG.5, C₀=10.2, and C_(ave)=5.1. Therefore, theoretical unrelaxed stress(σ₀) was approximately over 300 MPa when ignoring stress relaxation,assuming B was about 0.6 ppk/mol %. (As published in Journal ofNon-Crystalline Solids, 358 (2012) 316-320 by Tandia et al.) In thiscited paper, the authors dealt with Na+4 K+IOX, the coefficient B wasapproximately 1 ppk/mol %. Based on ionic radius of Li+(0.08 nm),Na+(0.102 nm), and K+(0.0138 nm), one mol % percent of Li+4 Na+IOXcauses about 60% growth when compared to one mol % percent of Na+4K+,therefore a value of 0.6 ppk/mol % Li+4 Na+was used for B. E was 83 GPaand v was 0.22. The measured stress profile in FIG. 4 for Example 1shows a surface stress (measured relaxed stress (σ_(r))) of about 115MPa when ignoring the surface steep profile. Therefore, the stressrelaxation in this example was about 60% (e.g., (300−115)/300).

The retained strength of the article of Example 1 was determined in a4-point bending (4PB) after damage introduction by a surface impact testin accordance with the methods discussed above. In a first set ofexperiments, a first retained strength was determined relative to damageimpact by 30 grit sandpaper. In a second independent set of experiments,a second retained strength was determined relative to damage impact by80 grit sandpaper.

FIG. 6 is a plot of applied fracture stress (MPa) versus grit forExample 1, where for 30 grit, the first retained strength averaged 185MPa, and for 80 grit, the second retained strength averaged 189 MPa. 30grit sandpaper generally introduces significantly deeper damage ascompared to 80 grit sandpaper. For Example 1, it was unexpectedly foundthat the second retained strength after impact at 30 grit wasstatistically equivalent to (e.g., within 5 MPa of) the first retainedstrength after impact with 80 grit.

Example 3

Table 4 provides a summary of dual ion exchange (DIOX) conditions usingnitrate salts of potassium (K) and sodium (Na), as noted, for Example 3.A substrate according to composition A having a thickness of 800micrometers was used. The DIOX conditions included a preheat at 380° C.for 10 minutes. Also shown in Table 4 is data for: compressive stress(CS), knee depth of layer (DOL_(k)), and central tension (CT) after StepII. After Step I, CS as 540.0 MPa and DOL_(k) was 6.50 m. Both Step Iand Step II included the addition of 0.5 wt. % silicic acid to the IOXbath. Between Step I and Step II, the substrate was cleaned to removeexcess salt.

TABLE 4 DIOX CS DOL_(k) CT DOC EXAMPLE Substrate Step I* Step II* (MPa)(μm) (MPa) (μm) 3 A 60 wt % K/ 100 wt % K 872.0 7.10 146 202 40 wt % Na,500° C., 0.25 t 450° C., 45 minutes 10hours *Each of Step I and Step IIincluded the addition of 0.5 wt. % silicic acid.

FIG. 7 provides a smoothed stress profile (stress (MPa) versus depth(micrometers)) for Example 3 after Step II. In this example, in order toaccount for variability in measurements, the stress versus depth datawas smoothed in accordance with the following equation:y=9E−13x⁶−1E−09x⁵+6E−07x⁴−0.0001x³+0.0084x²−0.0475x+113.15; R²=0.9998.FIG. 8 is a graph of the second derivative of the stress profile plot ofFIG. 7. Starting at about a depth of 50 micrometers, the secondderivative remains negative until about the center of the article (400micrometers) with the exception of some positive values in the range of63 to 64 micrometers. In the depth range from 50 micrometers to 202micrometers (the DOC), the absolute value of the second derivative wasin the range of 0.03 to 0.70.

Example 3 was annealed at 500° C. after DIOX. Table 5 provides the CTdata.

TABLE 5 Annealing time CT EXAMPLE (minutes) (MPa) 3 20 125

FIG. 9 is an excerpt of the stress profile for Example 3 after annealingto show the parabolic region being fit to the following equation:

Stress(x)=2.317E−03x ²−2.099E+00x+3.403E+02, where R ²=9.987E−01.

Examples 5-8

The composition dependence of T_(g)(x) and m(x) of glass-basedsubstrates are based on experimentally determined values and a range wasevaluated using the modeling resulting from equations (1) to (7). Forthese examples, T_(g) was in the range of 550° C. to 650° C. andfragility index was in the range of 25 to 35. T_(f) was investigated inranges such that: 30° C. <T_(f)-T_(g)<70° C. Table 6 provides a summaryof the combinations.

TABLE 6 EXAMPLE T_(g) (° C.) m 5 650 35 6 650 25 7 550 35 8 550 25

Stress relaxation rates at 1 hour for T_(IOX) (IOX temperature) versusT_(f)−T_(g) (e.g., the difference between T_(f) and T_(g)) are plottedin FIGS. 10-13. The stress relaxation rates were calculated for theglass-based substrates according to Equation (1).

Stress relaxation rates of greater than or equal to 10%, for example, inthe range of 20% to 80%, and all values and subranges therebetween, andIOX treatment temperature of below 550° C., including below 500° C., aredesired. With respect to FIGS. 11-15, for a T_(IOX) temperature being500° C., a correlation between T_(g), minimum fragility mm and minimumfictive temperature (T_(f)-T_(g)) can be determined, as shown in FIG.15. For T_(IOX) of less than or equal to 500° C. to achieve desiredstress relaxation, a combination of T_(g) of less than or equal to 650°C., the difference between T_(f) and T_(g) (T_(f)−T_(g)) of greater thanor equal to 30° C., and m greater than or equal to 25 may be used asshown in Table 7 based on FIG. 15.

TABLE 7 Tf − Tg 70 60 50 40 30 Tg Minimum m 650 27.6 29.7 34.2 >35 >35600 25.7 27.3 30.5 >35 >35 550 23.6 24.1 25.1 27.8 35.0

All compositional components, relationships, and ratios described inthis specification are provided in mol % unless otherwise stated. Allranges disclosed in this specification include any and all ranges andsubranges encompassed by the broadly disclosed ranges whether or notexplicitly stated before or after a range is disclosed.

While the foregoing is directed to various embodiments, other andfurther embodiments of the disclosure may be devised without departingfrom the basic scope thereof, and the scope thereof is determined by theclaims that follow. The features of the present disclosure may becombined in any and all combinations, for example as set forth in thefollowing numbered embodiments.

Embodiment 1. A glass-based substrate comprising: a glass transitiontemperature (T_(g)), a liquid fragility index (m), and fictivetemperature (T_(f)), wherein T_(g) is less than or equal to 650° C., avalue of T_(f) minus T_(g) is greater than or equal to −30° C., and m isgreater than or equal to 25.

Embodiment 2. The glass-based substrate of embodiment 1 comprising astress relaxation rate of greater than or equal to 10%.

Embodiment 3. The glass-based substrate of embodiment 1 or 2, whereinT_(g) is greater than or equal to 550° C., the value of T_(f) minusT_(g) is less than or equal to 100° C., and m is greater than or equalto 25.

Embodiment 4. The glass-based substrate of any preceding embodiment,wherein m is greater than or equal to 30.

Embodiment 5. The glass-based substrate of any preceding embodiment,wherein m is less than or equal to 60.

Embodiment 6. The glass-based substrate of embodiment 1 furthercomprising a lithium-based aluminosilicate composition and a fracturetoughness that is greater than or equal to 0.75 MPa*m^(0.5).

Embodiment 7. The glass-based substrate of embodiment 6, wherein thelithium-based aluminosilicate composition comprises a lithium oxide(Li₂O) content of greater than 8 mol %.

Embodiment 8. The glass-based substrate of embodiment 6, wherein thelithium-based aluminosilicate composition comprises a molar ratio ofsodium oxide (Na₂O) to lithium oxide (Li₂O) of less than 1.0.

Embodiment 9. The glass-based substrate of the preceding embodiment,wherein the molar ratio of sodium oxide (Na₂O) to lithium oxide (Li₂O)is less than or equal to 0.63.

Embodiment 10. The glass-based substrate of embodiment 6, wherein thelithium-based aluminosilicate composition comprises potassium oxide(K₂O) and phosphorus pentoxide (P₂O₅) in an amount that is less than 2mol % of the composition.

Embodiment 11. The glass-based substrate of any of embodiment 6 to thepreceding embodiment, wherein the lithium-based aluminosilicatecomposition comprises: 50 mol % to 69 mol % SiO₂; 12.5 mol % to 25 mol %Al₂O₃; 0 mol % to 8 mol % B₂O₃; greater than 0 mol % to 4 mol % CaO;greater than 0 mol % to 17.5 mol % MgO; 0.5 mol % to 8 mol % Na₂O; 0 mol% to 2.5 mol % La₂O₃; and greater than 8 mol % to 18 mol % Li₂O.

Embodiment 12. A method of manufacturing a glass-based articlecomprising: preparing a glass composition; exposing the glasscomposition to a process to form a glass-based substrate comprising: aglass transition temperature (T_(g)), a liquid fragility index (m), andfictive temperature (T_(f)), wherein T_(g) is less than or equal to 650°C., the difference between T_(f) and T_(g) is greater than or equal to−30° C., and m is greater than or equal to 25; and exposing theglass-based substrate to ion exchange conditions of less than or equalto 550° C., including less than or equal to 500° C., to form aglass-based article comprising a stress relaxation rate that is greaterthan or equal to 10%.

Embodiment 13. The method of the preceding embodiment, wherein theprocess to form the glass-based substrate comprises a float process, adown-draw process, a fusion-formable process, a slot-draw process, or aroll-form process.

Embodiment 14. The method of the preceding embodiment further comprisingan annealing step.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the embodiments describedherein without departing from the spirit and scope of the claimedsubject matter. Thus it is intended that the specification cover themodifications and variations of the various embodiments described hereinprovided such modification and variations come within the scope of theappended claims and their equivalents.

What is claimed is:
 1. A glass-based substrate comprising: a glasstransition temperature (T_(g)), a liquid fragility index (m), andfictive temperature (T_(f)), wherein T_(g) is less than or equal to 650°C., a value of T_(f) minus T_(g) is greater than or equal to −30° C.,and m is greater than or equal to
 25. 2. The glass-based substrate ofclaim 1 comprising a stress relaxation rate of greater than or equal to10%.
 3. The glass-based substrate of claim 1, wherein T_(g) is greaterthan or equal to 550° C., the value of T_(f) minus T_(g) is less than orequal to 100° C., and m is greater than or equal to
 25. 4. Theglass-based substrate of claim 1, wherein m is greater than or equal to30.
 5. The glass-based substrate of claim 1, wherein m is less than orequal to
 60. 6. The glass-based substrate of claim 1 further comprisinga lithium-based aluminosilicate composition and a fracture toughnessthat is greater than or equal to 0.75 MPa*m^(0.5).
 7. The glass-basedsubstrate of claim 6, wherein the lithium-based aluminosilicatecomposition comprises a lithium oxide (Li₂O) content of greater than 8mol %.
 8. The glass-based substrate of claim 6, wherein thelithium-based aluminosilicate composition comprises a molar ratio ofsodium oxide (Na₂O) to lithium oxide (Li₂O) of less than 1.0.
 9. Theglass-based substrate of claim 8, wherein the molar ratio of sodiumoxide (Na₂O) to lithium oxide (Li₂O) is less than or equal to 0.63. 10.The glass-based substrate of claim 6, wherein the lithium-basedaluminosilicate composition comprises potassium oxide (K₂O) andphosphorus pentoxide (P₂O₅) in an amount that is less than 2 mol % ofthe composition.
 11. The glass-based substrate of claim 6, wherein thelithium-based aluminosilicate composition comprises: 50 mol % to 69 mol% SiO₂; 12.5 mol % to 25 mol % Al₂O₃; 0 mol % to 8 mol % B₂O₃; greaterthan 0 mol % to 4 mol % CaO; greater than 0 mol % to 17.5 mol % MgO; 0.5mol % to 8 mol % Na₂O; 0 mol % to 2.5 mol % La₂O₃; and greater than 8mol % to 18 mol % Li₂O.
 12. A method of manufacturing a glass-basedarticle comprising: preparing a glass composition; exposing the glasscomposition to a process to form a glass-based substrate comprising: aglass transition temperature (T_(g)), a liquid fragility index (m), andfictive temperature (T_(f)), wherein T_(g) is less than or equal to 650°C., the difference between T_(f) and T_(g) is greater than or equal to−30° C., and m is greater than or equal to 25; and exposing theglass-based substrate to ion exchange conditions of less than or equalto 550° C. to form a glass-based article comprising a stress relaxationrate that is greater than or equal to 10%.
 13. The method of claim 12,wherein the process to form the glass-based substrate comprises a floatprocess, a down-draw process, a fusion-formable process, a slot-drawprocess, or a roll-form process.
 14. The method of claim 13 furthercomprising an annealing step.